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The sentence is rather confusing. I am not sure what you mean by saying that he could not "stand up to see her position." Choosing "stand up" and "see" together makes one wonder if the man just isn't tall enough. Do you mean that he couldn't stand up for her, that he did not agree with her position on the matter? If so, then I don't see the irony between that and acting cold toward her. Irony means that the two things are the opposite of each other. Not standing up for someone and being cold toward that person are very similar. While "ironic" and "ironical" are both adjectives, I believe that you would use the former here.